PROFINITE COMPLETION OF GRIGORCHUK'S GROUP IS NOT FINITELY PRESENTED

Benli M. G.

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, cilt.22, sa.5, 2012 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 5
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1142/s0218196712500452
  • Dergi Adı: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Grigorchuk group, profinite completion, BRANCH GROUPS, PRESENTATIONS
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

In this paper we prove that the profinite completion (G) over cap of the Grigorchuk group G is not finitely presented as a profinite group. We obtain this result by showing that H-2((G) over cap, F-2) is infinite dimensional. Also several results are proven about the finite quotients G/St(G)(n) including minimal presentations and Schur Multipliers.